Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data

• 成果类型: Article
• 署名作者: Bai, Jushan; Ng, Serena
• 署名单位: Columbia University; National Bureau of Economic Research
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1967163
• 发表日期: 2021
• 页码: 1746-1763
• 关键词: maximum-likelihood-estimation; factor models; inference; algorithm; VALUES; number

摘要

This article proposes an imputation procedure that uses the factors estimated from a tall block along with the re-rotated loadings estimated from a wide block to impute missing values in a panel of data. Assuming that a strong factor structure holds for the full panel of data and its sub-blocks, it is shown that the common component can be consistently estimated at four different rates of convergence without requiring regularization or iteration. An asymptotic analysis of the estimation error is obtained. An application of our analysis is estimation of counterfactuals when potential outcomes have a factor structure. We study the estimation of average and individual treatment effects on the treated and establish a normal distribution theory that can be useful for hypothesis testing.